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<FONT color="green">001</FONT>    /*<a name="line.1"></a>
<FONT color="green">002</FONT>     * Licensed to the Apache Software Foundation (ASF) under one or more<a name="line.2"></a>
<FONT color="green">003</FONT>     * contributor license agreements.  See the NOTICE file distributed with<a name="line.3"></a>
<FONT color="green">004</FONT>     * this work for additional information regarding copyright ownership.<a name="line.4"></a>
<FONT color="green">005</FONT>     * The ASF licenses this file to You under the Apache License, Version 2.0<a name="line.5"></a>
<FONT color="green">006</FONT>     * (the "License"); you may not use this file except in compliance with<a name="line.6"></a>
<FONT color="green">007</FONT>     * the License.  You may obtain a copy of the License at<a name="line.7"></a>
<FONT color="green">008</FONT>     *<a name="line.8"></a>
<FONT color="green">009</FONT>     *      http://www.apache.org/licenses/LICENSE-2.0<a name="line.9"></a>
<FONT color="green">010</FONT>     *<a name="line.10"></a>
<FONT color="green">011</FONT>     * Unless required by applicable law or agreed to in writing, software<a name="line.11"></a>
<FONT color="green">012</FONT>     * distributed under the License is distributed on an "AS IS" BASIS,<a name="line.12"></a>
<FONT color="green">013</FONT>     * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.<a name="line.13"></a>
<FONT color="green">014</FONT>     * See the License for the specific language governing permissions and<a name="line.14"></a>
<FONT color="green">015</FONT>     * limitations under the License.<a name="line.15"></a>
<FONT color="green">016</FONT>     */<a name="line.16"></a>
<FONT color="green">017</FONT>    package org.apache.commons.math.analysis.interpolation;<a name="line.17"></a>
<FONT color="green">018</FONT>    <a name="line.18"></a>
<FONT color="green">019</FONT>    import org.apache.commons.math.DimensionMismatchException;<a name="line.19"></a>
<FONT color="green">020</FONT>    import org.apache.commons.math.FunctionEvaluationException;<a name="line.20"></a>
<FONT color="green">021</FONT>    import org.apache.commons.math.analysis.BivariateRealFunction;<a name="line.21"></a>
<FONT color="green">022</FONT>    import org.apache.commons.math.exception.NoDataException;<a name="line.22"></a>
<FONT color="green">023</FONT>    import org.apache.commons.math.exception.OutOfRangeException;<a name="line.23"></a>
<FONT color="green">024</FONT>    import org.apache.commons.math.util.MathUtils;<a name="line.24"></a>
<FONT color="green">025</FONT>    <a name="line.25"></a>
<FONT color="green">026</FONT>    /**<a name="line.26"></a>
<FONT color="green">027</FONT>     * Function that implements the<a name="line.27"></a>
<FONT color="green">028</FONT>     * &lt;a href="http://en.wikipedia.org/wiki/Bicubic_interpolation"&gt;<a name="line.28"></a>
<FONT color="green">029</FONT>     * bicubic spline interpolation&lt;/a&gt;.<a name="line.29"></a>
<FONT color="green">030</FONT>     *<a name="line.30"></a>
<FONT color="green">031</FONT>     * @version $Revision$ $Date$<a name="line.31"></a>
<FONT color="green">032</FONT>     * @since 2.1<a name="line.32"></a>
<FONT color="green">033</FONT>     */<a name="line.33"></a>
<FONT color="green">034</FONT>    public class BicubicSplineInterpolatingFunction<a name="line.34"></a>
<FONT color="green">035</FONT>        implements BivariateRealFunction {<a name="line.35"></a>
<FONT color="green">036</FONT>        /**<a name="line.36"></a>
<FONT color="green">037</FONT>         * Matrix to compute the spline coefficients from the function values<a name="line.37"></a>
<FONT color="green">038</FONT>         * and function derivatives values<a name="line.38"></a>
<FONT color="green">039</FONT>         */<a name="line.39"></a>
<FONT color="green">040</FONT>        private static final double[][] AINV = {<a name="line.40"></a>
<FONT color="green">041</FONT>            { 1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0 },<a name="line.41"></a>
<FONT color="green">042</FONT>            { 0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0 },<a name="line.42"></a>
<FONT color="green">043</FONT>            { -3,3,0,0,-2,-1,0,0,0,0,0,0,0,0,0,0 },<a name="line.43"></a>
<FONT color="green">044</FONT>            { 2,-2,0,0,1,1,0,0,0,0,0,0,0,0,0,0 },<a name="line.44"></a>
<FONT color="green">045</FONT>            { 0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0 },<a name="line.45"></a>
<FONT color="green">046</FONT>            { 0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0 },<a name="line.46"></a>
<FONT color="green">047</FONT>            { 0,0,0,0,0,0,0,0,-3,3,0,0,-2,-1,0,0 },<a name="line.47"></a>
<FONT color="green">048</FONT>            { 0,0,0,0,0,0,0,0,2,-2,0,0,1,1,0,0 },<a name="line.48"></a>
<FONT color="green">049</FONT>            { -3,0,3,0,0,0,0,0,-2,0,-1,0,0,0,0,0 },<a name="line.49"></a>
<FONT color="green">050</FONT>            { 0,0,0,0,-3,0,3,0,0,0,0,0,-2,0,-1,0 },<a name="line.50"></a>
<FONT color="green">051</FONT>            { 9,-9,-9,9,6,3,-6,-3,6,-6,3,-3,4,2,2,1 },<a name="line.51"></a>
<FONT color="green">052</FONT>            { -6,6,6,-6,-3,-3,3,3,-4,4,-2,2,-2,-2,-1,-1 },<a name="line.52"></a>
<FONT color="green">053</FONT>            { 2,0,-2,0,0,0,0,0,1,0,1,0,0,0,0,0 },<a name="line.53"></a>
<FONT color="green">054</FONT>            { 0,0,0,0,2,0,-2,0,0,0,0,0,1,0,1,0 },<a name="line.54"></a>
<FONT color="green">055</FONT>            { -6,6,6,-6,-4,-2,4,2,-3,3,-3,3,-2,-1,-2,-1 },<a name="line.55"></a>
<FONT color="green">056</FONT>            { 4,-4,-4,4,2,2,-2,-2,2,-2,2,-2,1,1,1,1 }<a name="line.56"></a>
<FONT color="green">057</FONT>        };<a name="line.57"></a>
<FONT color="green">058</FONT>    <a name="line.58"></a>
<FONT color="green">059</FONT>        /** Samples x-coordinates */<a name="line.59"></a>
<FONT color="green">060</FONT>        private final double[] xval;<a name="line.60"></a>
<FONT color="green">061</FONT>        /** Samples y-coordinates */<a name="line.61"></a>
<FONT color="green">062</FONT>        private final double[] yval;<a name="line.62"></a>
<FONT color="green">063</FONT>        /** Set of cubic splines patching the whole data grid */<a name="line.63"></a>
<FONT color="green">064</FONT>        private final BicubicSplineFunction[][] splines;<a name="line.64"></a>
<FONT color="green">065</FONT>        /**<a name="line.65"></a>
<FONT color="green">066</FONT>         * Partial derivatives<a name="line.66"></a>
<FONT color="green">067</FONT>         * The value of the first index determines the kind of derivatives:<a name="line.67"></a>
<FONT color="green">068</FONT>         * 0 = first partial derivatives wrt x<a name="line.68"></a>
<FONT color="green">069</FONT>         * 1 = first partial derivatives wrt y<a name="line.69"></a>
<FONT color="green">070</FONT>         * 2 = second partial derivatives wrt x<a name="line.70"></a>
<FONT color="green">071</FONT>         * 3 = second partial derivatives wrt y<a name="line.71"></a>
<FONT color="green">072</FONT>         * 4 = cross partial derivatives<a name="line.72"></a>
<FONT color="green">073</FONT>         */<a name="line.73"></a>
<FONT color="green">074</FONT>        private BivariateRealFunction[][][] partialDerivatives = null;<a name="line.74"></a>
<FONT color="green">075</FONT>    <a name="line.75"></a>
<FONT color="green">076</FONT>        /**<a name="line.76"></a>
<FONT color="green">077</FONT>         * @param x Sample values of the x-coordinate, in increasing order.<a name="line.77"></a>
<FONT color="green">078</FONT>         * @param y Sample values of the y-coordinate, in increasing order.<a name="line.78"></a>
<FONT color="green">079</FONT>         * @param f Values of the function on every grid point.<a name="line.79"></a>
<FONT color="green">080</FONT>         * @param dFdX Values of the partial derivative of function with respect<a name="line.80"></a>
<FONT color="green">081</FONT>         * to x on every grid point.<a name="line.81"></a>
<FONT color="green">082</FONT>         * @param dFdY Values of the partial derivative of function with respect<a name="line.82"></a>
<FONT color="green">083</FONT>         * to y on every grid point.<a name="line.83"></a>
<FONT color="green">084</FONT>         * @param d2FdXdY Values of the cross partial derivative of function on<a name="line.84"></a>
<FONT color="green">085</FONT>         * every grid point.<a name="line.85"></a>
<FONT color="green">086</FONT>         * @throws DimensionMismatchException if the various arrays do not contain<a name="line.86"></a>
<FONT color="green">087</FONT>         * the expected number of elements.<a name="line.87"></a>
<FONT color="green">088</FONT>         * @throws org.apache.commons.math.exception.NonMonotonousSequenceException<a name="line.88"></a>
<FONT color="green">089</FONT>         * if {@code x} or {@code y} are not strictly increasing.<a name="line.89"></a>
<FONT color="green">090</FONT>         * @throws NoDataException if any of the arrays has zero length.<a name="line.90"></a>
<FONT color="green">091</FONT>         */<a name="line.91"></a>
<FONT color="green">092</FONT>        public BicubicSplineInterpolatingFunction(double[] x,<a name="line.92"></a>
<FONT color="green">093</FONT>                                                  double[] y,<a name="line.93"></a>
<FONT color="green">094</FONT>                                                  double[][] f,<a name="line.94"></a>
<FONT color="green">095</FONT>                                                  double[][] dFdX,<a name="line.95"></a>
<FONT color="green">096</FONT>                                                  double[][] dFdY,<a name="line.96"></a>
<FONT color="green">097</FONT>                                                  double[][] d2FdXdY)<a name="line.97"></a>
<FONT color="green">098</FONT>            throws DimensionMismatchException {<a name="line.98"></a>
<FONT color="green">099</FONT>            final int xLen = x.length;<a name="line.99"></a>
<FONT color="green">100</FONT>            final int yLen = y.length;<a name="line.100"></a>
<FONT color="green">101</FONT>    <a name="line.101"></a>
<FONT color="green">102</FONT>            if (xLen == 0 || yLen == 0 || f.length == 0 || f[0].length == 0) {<a name="line.102"></a>
<FONT color="green">103</FONT>                throw new NoDataException();<a name="line.103"></a>
<FONT color="green">104</FONT>            }<a name="line.104"></a>
<FONT color="green">105</FONT>            if (xLen != f.length) {<a name="line.105"></a>
<FONT color="green">106</FONT>                throw new DimensionMismatchException(xLen, f.length);<a name="line.106"></a>
<FONT color="green">107</FONT>            }<a name="line.107"></a>
<FONT color="green">108</FONT>            if (xLen != dFdX.length) {<a name="line.108"></a>
<FONT color="green">109</FONT>                throw new DimensionMismatchException(xLen, dFdX.length);<a name="line.109"></a>
<FONT color="green">110</FONT>            }<a name="line.110"></a>
<FONT color="green">111</FONT>            if (xLen != dFdY.length) {<a name="line.111"></a>
<FONT color="green">112</FONT>                throw new DimensionMismatchException(xLen, dFdY.length);<a name="line.112"></a>
<FONT color="green">113</FONT>            }<a name="line.113"></a>
<FONT color="green">114</FONT>            if (xLen != d2FdXdY.length) {<a name="line.114"></a>
<FONT color="green">115</FONT>                throw new DimensionMismatchException(xLen, d2FdXdY.length);<a name="line.115"></a>
<FONT color="green">116</FONT>            }<a name="line.116"></a>
<FONT color="green">117</FONT>    <a name="line.117"></a>
<FONT color="green">118</FONT>            MathUtils.checkOrder(x);<a name="line.118"></a>
<FONT color="green">119</FONT>            MathUtils.checkOrder(y);<a name="line.119"></a>
<FONT color="green">120</FONT>    <a name="line.120"></a>
<FONT color="green">121</FONT>            xval = x.clone();<a name="line.121"></a>
<FONT color="green">122</FONT>            yval = y.clone();<a name="line.122"></a>
<FONT color="green">123</FONT>    <a name="line.123"></a>
<FONT color="green">124</FONT>            final int lastI = xLen - 1;<a name="line.124"></a>
<FONT color="green">125</FONT>            final int lastJ = yLen - 1;<a name="line.125"></a>
<FONT color="green">126</FONT>            splines = new BicubicSplineFunction[lastI][lastJ];<a name="line.126"></a>
<FONT color="green">127</FONT>    <a name="line.127"></a>
<FONT color="green">128</FONT>            for (int i = 0; i &lt; lastI; i++) {<a name="line.128"></a>
<FONT color="green">129</FONT>                if (f[i].length != yLen) {<a name="line.129"></a>
<FONT color="green">130</FONT>                    throw new DimensionMismatchException(f[i].length, yLen);<a name="line.130"></a>
<FONT color="green">131</FONT>                }<a name="line.131"></a>
<FONT color="green">132</FONT>                if (dFdX[i].length != yLen) {<a name="line.132"></a>
<FONT color="green">133</FONT>                    throw new DimensionMismatchException(dFdX[i].length, yLen);<a name="line.133"></a>
<FONT color="green">134</FONT>                }<a name="line.134"></a>
<FONT color="green">135</FONT>                if (dFdY[i].length != yLen) {<a name="line.135"></a>
<FONT color="green">136</FONT>                    throw new DimensionMismatchException(dFdY[i].length, yLen);<a name="line.136"></a>
<FONT color="green">137</FONT>                }<a name="line.137"></a>
<FONT color="green">138</FONT>                if (d2FdXdY[i].length != yLen) {<a name="line.138"></a>
<FONT color="green">139</FONT>                    throw new DimensionMismatchException(d2FdXdY[i].length, yLen);<a name="line.139"></a>
<FONT color="green">140</FONT>                }<a name="line.140"></a>
<FONT color="green">141</FONT>                final int ip1 = i + 1;<a name="line.141"></a>
<FONT color="green">142</FONT>                for (int j = 0; j &lt; lastJ; j++) {<a name="line.142"></a>
<FONT color="green">143</FONT>                    final int jp1 = j + 1;<a name="line.143"></a>
<FONT color="green">144</FONT>                    final double[] beta = new double[] {<a name="line.144"></a>
<FONT color="green">145</FONT>                        f[i][j], f[ip1][j], f[i][jp1], f[ip1][jp1],<a name="line.145"></a>
<FONT color="green">146</FONT>                        dFdX[i][j], dFdX[ip1][j], dFdX[i][jp1], dFdX[ip1][jp1],<a name="line.146"></a>
<FONT color="green">147</FONT>                        dFdY[i][j], dFdY[ip1][j], dFdY[i][jp1], dFdY[ip1][jp1],<a name="line.147"></a>
<FONT color="green">148</FONT>                        d2FdXdY[i][j], d2FdXdY[ip1][j], d2FdXdY[i][jp1], d2FdXdY[ip1][jp1]<a name="line.148"></a>
<FONT color="green">149</FONT>                    };<a name="line.149"></a>
<FONT color="green">150</FONT>    <a name="line.150"></a>
<FONT color="green">151</FONT>                    splines[i][j] = new BicubicSplineFunction(computeSplineCoefficients(beta));<a name="line.151"></a>
<FONT color="green">152</FONT>                }<a name="line.152"></a>
<FONT color="green">153</FONT>            }<a name="line.153"></a>
<FONT color="green">154</FONT>        }<a name="line.154"></a>
<FONT color="green">155</FONT>    <a name="line.155"></a>
<FONT color="green">156</FONT>        /**<a name="line.156"></a>
<FONT color="green">157</FONT>         * {@inheritDoc}<a name="line.157"></a>
<FONT color="green">158</FONT>         */<a name="line.158"></a>
<FONT color="green">159</FONT>        public double value(double x, double y) {<a name="line.159"></a>
<FONT color="green">160</FONT>            final int i = searchIndex(x, xval);<a name="line.160"></a>
<FONT color="green">161</FONT>            if (i == -1) {<a name="line.161"></a>
<FONT color="green">162</FONT>                throw new OutOfRangeException(x, xval[0], xval[xval.length - 1]);<a name="line.162"></a>
<FONT color="green">163</FONT>            }<a name="line.163"></a>
<FONT color="green">164</FONT>            final int j = searchIndex(y, yval);<a name="line.164"></a>
<FONT color="green">165</FONT>            if (j == -1) {<a name="line.165"></a>
<FONT color="green">166</FONT>                throw new OutOfRangeException(y, yval[0], yval[yval.length - 1]);<a name="line.166"></a>
<FONT color="green">167</FONT>            }<a name="line.167"></a>
<FONT color="green">168</FONT>    <a name="line.168"></a>
<FONT color="green">169</FONT>            final double xN = (x - xval[i]) / (xval[i + 1] - xval[i]);<a name="line.169"></a>
<FONT color="green">170</FONT>            final double yN = (y - yval[j]) / (yval[j + 1] - yval[j]);<a name="line.170"></a>
<FONT color="green">171</FONT>    <a name="line.171"></a>
<FONT color="green">172</FONT>            return splines[i][j].value(xN, yN);<a name="line.172"></a>
<FONT color="green">173</FONT>        }<a name="line.173"></a>
<FONT color="green">174</FONT>    <a name="line.174"></a>
<FONT color="green">175</FONT>        /**<a name="line.175"></a>
<FONT color="green">176</FONT>         * @param x x-coordinate.<a name="line.176"></a>
<FONT color="green">177</FONT>         * @param y y-coordinate.<a name="line.177"></a>
<FONT color="green">178</FONT>         * @return the value at point (x, y) of the first partial derivative with<a name="line.178"></a>
<FONT color="green">179</FONT>         * respect to x.<a name="line.179"></a>
<FONT color="green">180</FONT>         * @since 2.2<a name="line.180"></a>
<FONT color="green">181</FONT>         */<a name="line.181"></a>
<FONT color="green">182</FONT>        public double partialDerivativeX(double x, double y) {<a name="line.182"></a>
<FONT color="green">183</FONT>            return partialDerivative(0, x, y);<a name="line.183"></a>
<FONT color="green">184</FONT>        }<a name="line.184"></a>
<FONT color="green">185</FONT>        /**<a name="line.185"></a>
<FONT color="green">186</FONT>         * @param x x-coordinate.<a name="line.186"></a>
<FONT color="green">187</FONT>         * @param y y-coordinate.<a name="line.187"></a>
<FONT color="green">188</FONT>         * @return the value at point (x, y) of the first partial derivative with<a name="line.188"></a>
<FONT color="green">189</FONT>         * respect to y.<a name="line.189"></a>
<FONT color="green">190</FONT>         * @since 2.2<a name="line.190"></a>
<FONT color="green">191</FONT>         */<a name="line.191"></a>
<FONT color="green">192</FONT>        public double partialDerivativeY(double x, double y) {<a name="line.192"></a>
<FONT color="green">193</FONT>            return partialDerivative(1, x, y);<a name="line.193"></a>
<FONT color="green">194</FONT>        }<a name="line.194"></a>
<FONT color="green">195</FONT>        /**<a name="line.195"></a>
<FONT color="green">196</FONT>         * @param x x-coordinate.<a name="line.196"></a>
<FONT color="green">197</FONT>         * @param y y-coordinate.<a name="line.197"></a>
<FONT color="green">198</FONT>         * @return the value at point (x, y) of the second partial derivative with<a name="line.198"></a>
<FONT color="green">199</FONT>         * respect to x.<a name="line.199"></a>
<FONT color="green">200</FONT>         * @since 2.2<a name="line.200"></a>
<FONT color="green">201</FONT>         */<a name="line.201"></a>
<FONT color="green">202</FONT>        public double partialDerivativeXX(double x, double y) {<a name="line.202"></a>
<FONT color="green">203</FONT>            return partialDerivative(2, x, y);<a name="line.203"></a>
<FONT color="green">204</FONT>        }<a name="line.204"></a>
<FONT color="green">205</FONT>        /**<a name="line.205"></a>
<FONT color="green">206</FONT>         * @param x x-coordinate.<a name="line.206"></a>
<FONT color="green">207</FONT>         * @param y y-coordinate.<a name="line.207"></a>
<FONT color="green">208</FONT>         * @return the value at point (x, y) of the second partial derivative with<a name="line.208"></a>
<FONT color="green">209</FONT>         * respect to y.<a name="line.209"></a>
<FONT color="green">210</FONT>         * @since 2.2<a name="line.210"></a>
<FONT color="green">211</FONT>         */<a name="line.211"></a>
<FONT color="green">212</FONT>        public double partialDerivativeYY(double x, double y) {<a name="line.212"></a>
<FONT color="green">213</FONT>            return partialDerivative(3, x, y);<a name="line.213"></a>
<FONT color="green">214</FONT>        }<a name="line.214"></a>
<FONT color="green">215</FONT>        /**<a name="line.215"></a>
<FONT color="green">216</FONT>         * @param x x-coordinate.<a name="line.216"></a>
<FONT color="green">217</FONT>         * @param y y-coordinate.<a name="line.217"></a>
<FONT color="green">218</FONT>         * @return the value at point (x, y) of the second partial cross-derivative.<a name="line.218"></a>
<FONT color="green">219</FONT>         * @since 2.2<a name="line.219"></a>
<FONT color="green">220</FONT>         */<a name="line.220"></a>
<FONT color="green">221</FONT>        public double partialDerivativeXY(double x, double y) {<a name="line.221"></a>
<FONT color="green">222</FONT>            return partialDerivative(4, x, y);<a name="line.222"></a>
<FONT color="green">223</FONT>        }<a name="line.223"></a>
<FONT color="green">224</FONT>    <a name="line.224"></a>
<FONT color="green">225</FONT>        /**<a name="line.225"></a>
<FONT color="green">226</FONT>         * @param which First index in {@link #partialDerivatives}.<a name="line.226"></a>
<FONT color="green">227</FONT>         * @param x x-coordinate.<a name="line.227"></a>
<FONT color="green">228</FONT>         * @param y y-coordinate.<a name="line.228"></a>
<FONT color="green">229</FONT>         * @return the value at point (x, y) of the selected partial derivative.<a name="line.229"></a>
<FONT color="green">230</FONT>         * @throws FunctionEvaluationException<a name="line.230"></a>
<FONT color="green">231</FONT>         */<a name="line.231"></a>
<FONT color="green">232</FONT>        private double partialDerivative(int which, double x, double y) {<a name="line.232"></a>
<FONT color="green">233</FONT>            if (partialDerivatives == null) {<a name="line.233"></a>
<FONT color="green">234</FONT>                computePartialDerivatives();<a name="line.234"></a>
<FONT color="green">235</FONT>            }<a name="line.235"></a>
<FONT color="green">236</FONT>    <a name="line.236"></a>
<FONT color="green">237</FONT>            final int i = searchIndex(x, xval);<a name="line.237"></a>
<FONT color="green">238</FONT>            if (i == -1) {<a name="line.238"></a>
<FONT color="green">239</FONT>                throw new OutOfRangeException(x, xval[0], xval[xval.length - 1]);<a name="line.239"></a>
<FONT color="green">240</FONT>            }<a name="line.240"></a>
<FONT color="green">241</FONT>            final int j = searchIndex(y, yval);<a name="line.241"></a>
<FONT color="green">242</FONT>            if (j == -1) {<a name="line.242"></a>
<FONT color="green">243</FONT>                throw new OutOfRangeException(y, yval[0], yval[yval.length - 1]);<a name="line.243"></a>
<FONT color="green">244</FONT>            }<a name="line.244"></a>
<FONT color="green">245</FONT>    <a name="line.245"></a>
<FONT color="green">246</FONT>            final double xN = (x - xval[i]) / (xval[i + 1] - xval[i]);<a name="line.246"></a>
<FONT color="green">247</FONT>            final double yN = (y - yval[j]) / (yval[j + 1] - yval[j]);<a name="line.247"></a>
<FONT color="green">248</FONT>    <a name="line.248"></a>
<FONT color="green">249</FONT>            try {<a name="line.249"></a>
<FONT color="green">250</FONT>                return partialDerivatives[which][i][j].value(xN, yN);<a name="line.250"></a>
<FONT color="green">251</FONT>            } catch (FunctionEvaluationException fee) {<a name="line.251"></a>
<FONT color="green">252</FONT>                // this should never happen<a name="line.252"></a>
<FONT color="green">253</FONT>                throw new RuntimeException(fee);<a name="line.253"></a>
<FONT color="green">254</FONT>            }<a name="line.254"></a>
<FONT color="green">255</FONT>    <a name="line.255"></a>
<FONT color="green">256</FONT>        }<a name="line.256"></a>
<FONT color="green">257</FONT>    <a name="line.257"></a>
<FONT color="green">258</FONT>        /**<a name="line.258"></a>
<FONT color="green">259</FONT>         * Compute all partial derivatives.<a name="line.259"></a>
<FONT color="green">260</FONT>         */<a name="line.260"></a>
<FONT color="green">261</FONT>        private void computePartialDerivatives() {<a name="line.261"></a>
<FONT color="green">262</FONT>            final int lastI = xval.length - 1;<a name="line.262"></a>
<FONT color="green">263</FONT>            final int lastJ = yval.length - 1;<a name="line.263"></a>
<FONT color="green">264</FONT>            partialDerivatives = new BivariateRealFunction[5][lastI][lastJ];<a name="line.264"></a>
<FONT color="green">265</FONT>    <a name="line.265"></a>
<FONT color="green">266</FONT>            for (int i = 0; i &lt; lastI; i++) {<a name="line.266"></a>
<FONT color="green">267</FONT>                for (int j = 0; j &lt; lastJ; j++) {<a name="line.267"></a>
<FONT color="green">268</FONT>                    final BicubicSplineFunction f = splines[i][j];<a name="line.268"></a>
<FONT color="green">269</FONT>                    partialDerivatives[0][i][j] = f.partialDerivativeX();<a name="line.269"></a>
<FONT color="green">270</FONT>                    partialDerivatives[1][i][j] = f.partialDerivativeY();<a name="line.270"></a>
<FONT color="green">271</FONT>                    partialDerivatives[2][i][j] = f.partialDerivativeXX();<a name="line.271"></a>
<FONT color="green">272</FONT>                    partialDerivatives[3][i][j] = f.partialDerivativeYY();<a name="line.272"></a>
<FONT color="green">273</FONT>                    partialDerivatives[4][i][j] = f.partialDerivativeXY();<a name="line.273"></a>
<FONT color="green">274</FONT>                }<a name="line.274"></a>
<FONT color="green">275</FONT>            }<a name="line.275"></a>
<FONT color="green">276</FONT>        }<a name="line.276"></a>
<FONT color="green">277</FONT>    <a name="line.277"></a>
<FONT color="green">278</FONT>        /**<a name="line.278"></a>
<FONT color="green">279</FONT>         * @param c Coordinate.<a name="line.279"></a>
<FONT color="green">280</FONT>         * @param val Coordinate samples.<a name="line.280"></a>
<FONT color="green">281</FONT>         * @return the index in {@code val} corresponding to the interval<a name="line.281"></a>
<FONT color="green">282</FONT>         * containing {@code c}, or {@code -1} if {@code c} is out of the<a name="line.282"></a>
<FONT color="green">283</FONT>         * range defined by the end values of {@code val}.<a name="line.283"></a>
<FONT color="green">284</FONT>         */<a name="line.284"></a>
<FONT color="green">285</FONT>        private int searchIndex(double c, double[] val) {<a name="line.285"></a>
<FONT color="green">286</FONT>            if (c &lt; val[0]) {<a name="line.286"></a>
<FONT color="green">287</FONT>                return -1;<a name="line.287"></a>
<FONT color="green">288</FONT>            }<a name="line.288"></a>
<FONT color="green">289</FONT>    <a name="line.289"></a>
<FONT color="green">290</FONT>            final int max = val.length;<a name="line.290"></a>
<FONT color="green">291</FONT>            for (int i = 1; i &lt; max; i++) {<a name="line.291"></a>
<FONT color="green">292</FONT>                if (c &lt;= val[i]) {<a name="line.292"></a>
<FONT color="green">293</FONT>                    return i - 1;<a name="line.293"></a>
<FONT color="green">294</FONT>                }<a name="line.294"></a>
<FONT color="green">295</FONT>            }<a name="line.295"></a>
<FONT color="green">296</FONT>    <a name="line.296"></a>
<FONT color="green">297</FONT>            return -1;<a name="line.297"></a>
<FONT color="green">298</FONT>        }<a name="line.298"></a>
<FONT color="green">299</FONT>    <a name="line.299"></a>
<FONT color="green">300</FONT>        /**<a name="line.300"></a>
<FONT color="green">301</FONT>         * Compute the spline coefficients from the list of function values and<a name="line.301"></a>
<FONT color="green">302</FONT>         * function partial derivatives values at the four corners of a grid<a name="line.302"></a>
<FONT color="green">303</FONT>         * element. They must be specified in the following order:<a name="line.303"></a>
<FONT color="green">304</FONT>         * &lt;ul&gt;<a name="line.304"></a>
<FONT color="green">305</FONT>         *  &lt;li&gt;f(0,0)&lt;/li&gt;<a name="line.305"></a>
<FONT color="green">306</FONT>         *  &lt;li&gt;f(1,0)&lt;/li&gt;<a name="line.306"></a>
<FONT color="green">307</FONT>         *  &lt;li&gt;f(0,1)&lt;/li&gt;<a name="line.307"></a>
<FONT color="green">308</FONT>         *  &lt;li&gt;f(1,1)&lt;/li&gt;<a name="line.308"></a>
<FONT color="green">309</FONT>         *  &lt;li&gt;f&lt;sub&gt;x&lt;/sub&gt;(0,0)&lt;/li&gt;<a name="line.309"></a>
<FONT color="green">310</FONT>         *  &lt;li&gt;f&lt;sub&gt;x&lt;/sub&gt;(1,0)&lt;/li&gt;<a name="line.310"></a>
<FONT color="green">311</FONT>         *  &lt;li&gt;f&lt;sub&gt;x&lt;/sub&gt;(0,1)&lt;/li&gt;<a name="line.311"></a>
<FONT color="green">312</FONT>         *  &lt;li&gt;f&lt;sub&gt;x&lt;/sub&gt;(1,1)&lt;/li&gt;<a name="line.312"></a>
<FONT color="green">313</FONT>         *  &lt;li&gt;f&lt;sub&gt;y&lt;/sub&gt;(0,0)&lt;/li&gt;<a name="line.313"></a>
<FONT color="green">314</FONT>         *  &lt;li&gt;f&lt;sub&gt;y&lt;/sub&gt;(1,0)&lt;/li&gt;<a name="line.314"></a>
<FONT color="green">315</FONT>         *  &lt;li&gt;f&lt;sub&gt;y&lt;/sub&gt;(0,1)&lt;/li&gt;<a name="line.315"></a>
<FONT color="green">316</FONT>         *  &lt;li&gt;f&lt;sub&gt;y&lt;/sub&gt;(1,1)&lt;/li&gt;<a name="line.316"></a>
<FONT color="green">317</FONT>         *  &lt;li&gt;f&lt;sub&gt;xy&lt;/sub&gt;(0,0)&lt;/li&gt;<a name="line.317"></a>
<FONT color="green">318</FONT>         *  &lt;li&gt;f&lt;sub&gt;xy&lt;/sub&gt;(1,0)&lt;/li&gt;<a name="line.318"></a>
<FONT color="green">319</FONT>         *  &lt;li&gt;f&lt;sub&gt;xy&lt;/sub&gt;(0,1)&lt;/li&gt;<a name="line.319"></a>
<FONT color="green">320</FONT>         *  &lt;li&gt;f&lt;sub&gt;xy&lt;/sub&gt;(1,1)&lt;/li&gt;<a name="line.320"></a>
<FONT color="green">321</FONT>         * &lt;/ul&gt;<a name="line.321"></a>
<FONT color="green">322</FONT>         * where the subscripts indicate the partial derivative with respect to<a name="line.322"></a>
<FONT color="green">323</FONT>         * the corresponding variable(s).<a name="line.323"></a>
<FONT color="green">324</FONT>         *<a name="line.324"></a>
<FONT color="green">325</FONT>         * @param beta List of function values and function partial derivatives<a name="line.325"></a>
<FONT color="green">326</FONT>         * values.<a name="line.326"></a>
<FONT color="green">327</FONT>         * @return the spline coefficients.<a name="line.327"></a>
<FONT color="green">328</FONT>         */<a name="line.328"></a>
<FONT color="green">329</FONT>        private double[] computeSplineCoefficients(double[] beta) {<a name="line.329"></a>
<FONT color="green">330</FONT>            final double[] a = new double[16];<a name="line.330"></a>
<FONT color="green">331</FONT>    <a name="line.331"></a>
<FONT color="green">332</FONT>            for (int i = 0; i &lt; 16; i++) {<a name="line.332"></a>
<FONT color="green">333</FONT>                double result = 0;<a name="line.333"></a>
<FONT color="green">334</FONT>                final double[] row = AINV[i];<a name="line.334"></a>
<FONT color="green">335</FONT>                for (int j = 0; j &lt; 16; j++) {<a name="line.335"></a>
<FONT color="green">336</FONT>                    result += row[j] * beta[j];<a name="line.336"></a>
<FONT color="green">337</FONT>                }<a name="line.337"></a>
<FONT color="green">338</FONT>                a[i] = result;<a name="line.338"></a>
<FONT color="green">339</FONT>            }<a name="line.339"></a>
<FONT color="green">340</FONT>    <a name="line.340"></a>
<FONT color="green">341</FONT>            return a;<a name="line.341"></a>
<FONT color="green">342</FONT>        }<a name="line.342"></a>
<FONT color="green">343</FONT>    }<a name="line.343"></a>
<FONT color="green">344</FONT>    <a name="line.344"></a>
<FONT color="green">345</FONT>    /**<a name="line.345"></a>
<FONT color="green">346</FONT>     * 2D-spline function.<a name="line.346"></a>
<FONT color="green">347</FONT>     *<a name="line.347"></a>
<FONT color="green">348</FONT>     * @version $Revision$ $Date$<a name="line.348"></a>
<FONT color="green">349</FONT>     */<a name="line.349"></a>
<FONT color="green">350</FONT>    class BicubicSplineFunction<a name="line.350"></a>
<FONT color="green">351</FONT>        implements BivariateRealFunction {<a name="line.351"></a>
<FONT color="green">352</FONT>    <a name="line.352"></a>
<FONT color="green">353</FONT>        /** Number of points. */<a name="line.353"></a>
<FONT color="green">354</FONT>        private static final short N = 4;<a name="line.354"></a>
<FONT color="green">355</FONT>    <a name="line.355"></a>
<FONT color="green">356</FONT>        /** Coefficients */<a name="line.356"></a>
<FONT color="green">357</FONT>        private final double[][] a;<a name="line.357"></a>
<FONT color="green">358</FONT>    <a name="line.358"></a>
<FONT color="green">359</FONT>        /** First partial derivative along x. */<a name="line.359"></a>
<FONT color="green">360</FONT>        private BivariateRealFunction partialDerivativeX;<a name="line.360"></a>
<FONT color="green">361</FONT>    <a name="line.361"></a>
<FONT color="green">362</FONT>        /** First partial derivative along y. */<a name="line.362"></a>
<FONT color="green">363</FONT>        private BivariateRealFunction partialDerivativeY;<a name="line.363"></a>
<FONT color="green">364</FONT>    <a name="line.364"></a>
<FONT color="green">365</FONT>        /** Second partial derivative along x. */<a name="line.365"></a>
<FONT color="green">366</FONT>        private BivariateRealFunction partialDerivativeXX;<a name="line.366"></a>
<FONT color="green">367</FONT>    <a name="line.367"></a>
<FONT color="green">368</FONT>        /** Second partial derivative along y. */<a name="line.368"></a>
<FONT color="green">369</FONT>        private BivariateRealFunction partialDerivativeYY;<a name="line.369"></a>
<FONT color="green">370</FONT>    <a name="line.370"></a>
<FONT color="green">371</FONT>        /** Second crossed partial derivative. */<a name="line.371"></a>
<FONT color="green">372</FONT>        private BivariateRealFunction partialDerivativeXY;<a name="line.372"></a>
<FONT color="green">373</FONT>    <a name="line.373"></a>
<FONT color="green">374</FONT>        /**<a name="line.374"></a>
<FONT color="green">375</FONT>         * Simple constructor.<a name="line.375"></a>
<FONT color="green">376</FONT>         * @param a Spline coefficients<a name="line.376"></a>
<FONT color="green">377</FONT>         */<a name="line.377"></a>
<FONT color="green">378</FONT>        public BicubicSplineFunction(double[] a) {<a name="line.378"></a>
<FONT color="green">379</FONT>            this.a = new double[N][N];<a name="line.379"></a>
<FONT color="green">380</FONT>            for (int i = 0; i &lt; N; i++) {<a name="line.380"></a>
<FONT color="green">381</FONT>                for (int j = 0; j &lt; N; j++) {<a name="line.381"></a>
<FONT color="green">382</FONT>                    this.a[i][j] = a[i + N * j];<a name="line.382"></a>
<FONT color="green">383</FONT>                }<a name="line.383"></a>
<FONT color="green">384</FONT>            }<a name="line.384"></a>
<FONT color="green">385</FONT>        }<a name="line.385"></a>
<FONT color="green">386</FONT>    <a name="line.386"></a>
<FONT color="green">387</FONT>        /**<a name="line.387"></a>
<FONT color="green">388</FONT>         * {@inheritDoc}<a name="line.388"></a>
<FONT color="green">389</FONT>         */<a name="line.389"></a>
<FONT color="green">390</FONT>        public double value(double x, double y) {<a name="line.390"></a>
<FONT color="green">391</FONT>            if (x &lt; 0 || x &gt; 1) {<a name="line.391"></a>
<FONT color="green">392</FONT>                throw new OutOfRangeException(x, 0, 1);<a name="line.392"></a>
<FONT color="green">393</FONT>            }<a name="line.393"></a>
<FONT color="green">394</FONT>            if (y &lt; 0 || y &gt; 1) {<a name="line.394"></a>
<FONT color="green">395</FONT>                throw new OutOfRangeException(y, 0, 1);<a name="line.395"></a>
<FONT color="green">396</FONT>            }<a name="line.396"></a>
<FONT color="green">397</FONT>    <a name="line.397"></a>
<FONT color="green">398</FONT>            final double x2 = x * x;<a name="line.398"></a>
<FONT color="green">399</FONT>            final double x3 = x2 * x;<a name="line.399"></a>
<FONT color="green">400</FONT>            final double[] pX = {1, x, x2, x3};<a name="line.400"></a>
<FONT color="green">401</FONT>    <a name="line.401"></a>
<FONT color="green">402</FONT>            final double y2 = y * y;<a name="line.402"></a>
<FONT color="green">403</FONT>            final double y3 = y2 * y;<a name="line.403"></a>
<FONT color="green">404</FONT>            final double[] pY = {1, y, y2, y3};<a name="line.404"></a>
<FONT color="green">405</FONT>    <a name="line.405"></a>
<FONT color="green">406</FONT>            return apply(pX, pY, a);<a name="line.406"></a>
<FONT color="green">407</FONT>        }<a name="line.407"></a>
<FONT color="green">408</FONT>    <a name="line.408"></a>
<FONT color="green">409</FONT>        /**<a name="line.409"></a>
<FONT color="green">410</FONT>         * Compute the value of the bicubic polynomial.<a name="line.410"></a>
<FONT color="green">411</FONT>         *<a name="line.411"></a>
<FONT color="green">412</FONT>         * @param pX Powers of the x-coordinate.<a name="line.412"></a>
<FONT color="green">413</FONT>         * @param pY Powers of the y-coordinate.<a name="line.413"></a>
<FONT color="green">414</FONT>         * @param coeff Spline coefficients.<a name="line.414"></a>
<FONT color="green">415</FONT>         * @return the interpolated value.<a name="line.415"></a>
<FONT color="green">416</FONT>         */<a name="line.416"></a>
<FONT color="green">417</FONT>        private double apply(double[] pX, double[] pY, double[][] coeff) {<a name="line.417"></a>
<FONT color="green">418</FONT>            double result = 0;<a name="line.418"></a>
<FONT color="green">419</FONT>            for (int i = 0; i &lt; N; i++) {<a name="line.419"></a>
<FONT color="green">420</FONT>                for (int j = 0; j &lt; N; j++) {<a name="line.420"></a>
<FONT color="green">421</FONT>                    result += coeff[i][j] * pX[i] * pY[j];<a name="line.421"></a>
<FONT color="green">422</FONT>                }<a name="line.422"></a>
<FONT color="green">423</FONT>            }<a name="line.423"></a>
<FONT color="green">424</FONT>    <a name="line.424"></a>
<FONT color="green">425</FONT>            return result;<a name="line.425"></a>
<FONT color="green">426</FONT>        }<a name="line.426"></a>
<FONT color="green">427</FONT>    <a name="line.427"></a>
<FONT color="green">428</FONT>        /**<a name="line.428"></a>
<FONT color="green">429</FONT>         * @return the partial derivative wrt {@code x}.<a name="line.429"></a>
<FONT color="green">430</FONT>         */<a name="line.430"></a>
<FONT color="green">431</FONT>        public BivariateRealFunction partialDerivativeX() {<a name="line.431"></a>
<FONT color="green">432</FONT>            if (partialDerivativeX == null) {<a name="line.432"></a>
<FONT color="green">433</FONT>                computePartialDerivatives();<a name="line.433"></a>
<FONT color="green">434</FONT>            }<a name="line.434"></a>
<FONT color="green">435</FONT>    <a name="line.435"></a>
<FONT color="green">436</FONT>            return partialDerivativeX;<a name="line.436"></a>
<FONT color="green">437</FONT>        }<a name="line.437"></a>
<FONT color="green">438</FONT>        /**<a name="line.438"></a>
<FONT color="green">439</FONT>         * @return the partial derivative wrt {@code y}.<a name="line.439"></a>
<FONT color="green">440</FONT>         */<a name="line.440"></a>
<FONT color="green">441</FONT>        public BivariateRealFunction partialDerivativeY() {<a name="line.441"></a>
<FONT color="green">442</FONT>            if (partialDerivativeY == null) {<a name="line.442"></a>
<FONT color="green">443</FONT>                computePartialDerivatives();<a name="line.443"></a>
<FONT color="green">444</FONT>            }<a name="line.444"></a>
<FONT color="green">445</FONT>    <a name="line.445"></a>
<FONT color="green">446</FONT>            return partialDerivativeY;<a name="line.446"></a>
<FONT color="green">447</FONT>        }<a name="line.447"></a>
<FONT color="green">448</FONT>        /**<a name="line.448"></a>
<FONT color="green">449</FONT>         * @return the second partial derivative wrt {@code x}.<a name="line.449"></a>
<FONT color="green">450</FONT>         */<a name="line.450"></a>
<FONT color="green">451</FONT>        public BivariateRealFunction partialDerivativeXX() {<a name="line.451"></a>
<FONT color="green">452</FONT>            if (partialDerivativeXX == null) {<a name="line.452"></a>
<FONT color="green">453</FONT>                computePartialDerivatives();<a name="line.453"></a>
<FONT color="green">454</FONT>            }<a name="line.454"></a>
<FONT color="green">455</FONT>    <a name="line.455"></a>
<FONT color="green">456</FONT>            return partialDerivativeXX;<a name="line.456"></a>
<FONT color="green">457</FONT>        }<a name="line.457"></a>
<FONT color="green">458</FONT>        /**<a name="line.458"></a>
<FONT color="green">459</FONT>         * @return the second partial derivative wrt {@code y}.<a name="line.459"></a>
<FONT color="green">460</FONT>         */<a name="line.460"></a>
<FONT color="green">461</FONT>        public BivariateRealFunction partialDerivativeYY() {<a name="line.461"></a>
<FONT color="green">462</FONT>            if (partialDerivativeYY == null) {<a name="line.462"></a>
<FONT color="green">463</FONT>                computePartialDerivatives();<a name="line.463"></a>
<FONT color="green">464</FONT>            }<a name="line.464"></a>
<FONT color="green">465</FONT>    <a name="line.465"></a>
<FONT color="green">466</FONT>            return partialDerivativeYY;<a name="line.466"></a>
<FONT color="green">467</FONT>        }<a name="line.467"></a>
<FONT color="green">468</FONT>        /**<a name="line.468"></a>
<FONT color="green">469</FONT>         * @return the second partial cross-derivative.<a name="line.469"></a>
<FONT color="green">470</FONT>         */<a name="line.470"></a>
<FONT color="green">471</FONT>        public BivariateRealFunction partialDerivativeXY() {<a name="line.471"></a>
<FONT color="green">472</FONT>            if (partialDerivativeXY == null) {<a name="line.472"></a>
<FONT color="green">473</FONT>                computePartialDerivatives();<a name="line.473"></a>
<FONT color="green">474</FONT>            }<a name="line.474"></a>
<FONT color="green">475</FONT>    <a name="line.475"></a>
<FONT color="green">476</FONT>            return partialDerivativeXY;<a name="line.476"></a>
<FONT color="green">477</FONT>        }<a name="line.477"></a>
<FONT color="green">478</FONT>    <a name="line.478"></a>
<FONT color="green">479</FONT>        /**<a name="line.479"></a>
<FONT color="green">480</FONT>         * Compute all partial derivatives functions.<a name="line.480"></a>
<FONT color="green">481</FONT>         */<a name="line.481"></a>
<FONT color="green">482</FONT>        private void computePartialDerivatives() {<a name="line.482"></a>
<FONT color="green">483</FONT>            final double[][] aX = new double[N][N];<a name="line.483"></a>
<FONT color="green">484</FONT>            final double[][] aY = new double[N][N];<a name="line.484"></a>
<FONT color="green">485</FONT>            final double[][] aXX = new double[N][N];<a name="line.485"></a>
<FONT color="green">486</FONT>            final double[][] aYY = new double[N][N];<a name="line.486"></a>
<FONT color="green">487</FONT>            final double[][] aXY = new double[N][N];<a name="line.487"></a>
<FONT color="green">488</FONT>    <a name="line.488"></a>
<FONT color="green">489</FONT>            for (int i = 0; i &lt; N; i++) {<a name="line.489"></a>
<FONT color="green">490</FONT>                for (int j = 0; j &lt; N; j++) {<a name="line.490"></a>
<FONT color="green">491</FONT>                    final double c = a[i][j];<a name="line.491"></a>
<FONT color="green">492</FONT>                    aX[i][j] = i * c;<a name="line.492"></a>
<FONT color="green">493</FONT>                    aY[i][j] = j * c;<a name="line.493"></a>
<FONT color="green">494</FONT>                    aXX[i][j] = (i - 1) * aX[i][j];<a name="line.494"></a>
<FONT color="green">495</FONT>                    aYY[i][j] = (j - 1) * aY[i][j];<a name="line.495"></a>
<FONT color="green">496</FONT>                    aXY[i][j] = j * aX[i][j];<a name="line.496"></a>
<FONT color="green">497</FONT>                }<a name="line.497"></a>
<FONT color="green">498</FONT>            }<a name="line.498"></a>
<FONT color="green">499</FONT>    <a name="line.499"></a>
<FONT color="green">500</FONT>            partialDerivativeX = new BivariateRealFunction() {<a name="line.500"></a>
<FONT color="green">501</FONT>                    public double value(double x, double y)  {<a name="line.501"></a>
<FONT color="green">502</FONT>                        final double x2 = x * x;<a name="line.502"></a>
<FONT color="green">503</FONT>                        final double[] pX = {0, 1, x, x2};<a name="line.503"></a>
<FONT color="green">504</FONT>    <a name="line.504"></a>
<FONT color="green">505</FONT>                        final double y2 = y * y;<a name="line.505"></a>
<FONT color="green">506</FONT>                        final double y3 = y2 * y;<a name="line.506"></a>
<FONT color="green">507</FONT>                        final double[] pY = {1, y, y2, y3};<a name="line.507"></a>
<FONT color="green">508</FONT>    <a name="line.508"></a>
<FONT color="green">509</FONT>                        return apply(pX, pY, aX);<a name="line.509"></a>
<FONT color="green">510</FONT>                    }<a name="line.510"></a>
<FONT color="green">511</FONT>                };<a name="line.511"></a>
<FONT color="green">512</FONT>            partialDerivativeY = new BivariateRealFunction() {<a name="line.512"></a>
<FONT color="green">513</FONT>                    public double value(double x, double y)  {<a name="line.513"></a>
<FONT color="green">514</FONT>                        final double x2 = x * x;<a name="line.514"></a>
<FONT color="green">515</FONT>                        final double x3 = x2 * x;<a name="line.515"></a>
<FONT color="green">516</FONT>                        final double[] pX = {1, x, x2, x3};<a name="line.516"></a>
<FONT color="green">517</FONT>    <a name="line.517"></a>
<FONT color="green">518</FONT>                        final double y2 = y * y;<a name="line.518"></a>
<FONT color="green">519</FONT>                        final double[] pY = {0, 1, y, y2};<a name="line.519"></a>
<FONT color="green">520</FONT>    <a name="line.520"></a>
<FONT color="green">521</FONT>                        return apply(pX, pY, aY);<a name="line.521"></a>
<FONT color="green">522</FONT>                    }<a name="line.522"></a>
<FONT color="green">523</FONT>                };<a name="line.523"></a>
<FONT color="green">524</FONT>            partialDerivativeXX = new BivariateRealFunction() {<a name="line.524"></a>
<FONT color="green">525</FONT>                    public double value(double x, double y)  {<a name="line.525"></a>
<FONT color="green">526</FONT>                        final double[] pX = {0, 0, 1, x};<a name="line.526"></a>
<FONT color="green">527</FONT>    <a name="line.527"></a>
<FONT color="green">528</FONT>                        final double y2 = y * y;<a name="line.528"></a>
<FONT color="green">529</FONT>                        final double y3 = y2 * y;<a name="line.529"></a>
<FONT color="green">530</FONT>                        final double[] pY = {1, y, y2, y3};<a name="line.530"></a>
<FONT color="green">531</FONT>    <a name="line.531"></a>
<FONT color="green">532</FONT>                        return apply(pX, pY, aXX);<a name="line.532"></a>
<FONT color="green">533</FONT>                    }<a name="line.533"></a>
<FONT color="green">534</FONT>                };<a name="line.534"></a>
<FONT color="green">535</FONT>            partialDerivativeYY = new BivariateRealFunction() {<a name="line.535"></a>
<FONT color="green">536</FONT>                    public double value(double x, double y)  {<a name="line.536"></a>
<FONT color="green">537</FONT>                        final double x2 = x * x;<a name="line.537"></a>
<FONT color="green">538</FONT>                        final double x3 = x2 * x;<a name="line.538"></a>
<FONT color="green">539</FONT>                        final double[] pX = {1, x, x2, x3};<a name="line.539"></a>
<FONT color="green">540</FONT>    <a name="line.540"></a>
<FONT color="green">541</FONT>                        final double[] pY = {0, 0, 1, y};<a name="line.541"></a>
<FONT color="green">542</FONT>    <a name="line.542"></a>
<FONT color="green">543</FONT>                        return apply(pX, pY, aYY);<a name="line.543"></a>
<FONT color="green">544</FONT>                    }<a name="line.544"></a>
<FONT color="green">545</FONT>                };<a name="line.545"></a>
<FONT color="green">546</FONT>            partialDerivativeXY = new BivariateRealFunction() {<a name="line.546"></a>
<FONT color="green">547</FONT>                    public double value(double x, double y)  {<a name="line.547"></a>
<FONT color="green">548</FONT>                        final double x2 = x * x;<a name="line.548"></a>
<FONT color="green">549</FONT>                        final double[] pX = {0, 1, x, x2};<a name="line.549"></a>
<FONT color="green">550</FONT>    <a name="line.550"></a>
<FONT color="green">551</FONT>                        final double y2 = y * y;<a name="line.551"></a>
<FONT color="green">552</FONT>                        final double[] pY = {0, 1, y, y2};<a name="line.552"></a>
<FONT color="green">553</FONT>    <a name="line.553"></a>
<FONT color="green">554</FONT>                        return apply(pX, pY, aXY);<a name="line.554"></a>
<FONT color="green">555</FONT>                    }<a name="line.555"></a>
<FONT color="green">556</FONT>                };<a name="line.556"></a>
<FONT color="green">557</FONT>        }<a name="line.557"></a>
<FONT color="green">558</FONT>    }<a name="line.558"></a>




























































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